wow... getting a little warm in here. I think it best not to make assumptions about all of the classical folks...
As for the overtone series it was well defined in terms of musical intervals.. Be aware that it also corresponds to 1, 2, 3, 4, etc.. times the fundamental frequency.
Look at the series based on 100 Hz because it is easy to calculate.
100 Hz fundamental. 200 Hz 2nd overtone (a doubling is an octave). 300 Hz 3rd overtone (octave plus a 5th roughly), 400 Hz 4th overtone (2 octaves or 1 octave plus a 5th plus a 4th), etc...
--Ben